Current work deals with the generated entropy of alumina–water nanofluid in a ribbed passage to cool the photovoltaic (PV) cell. The two-phase mixture approach is employed to model the nanofluid within a ribbed channel with discrete V-form and staggered rib roughness. The nanofluid is analysed at a concentration of 1%, and the outcomes are compared to pure water. This study focuses on the influences of the cross-section shape of the ribs. Four different shapes of the rib cross-section, including circular, elliptical, square, and triangularshaped, are investigated in this paper. The results indicated that using the nanofluid rather than water considerably reduces the thermally generated entropy such that the highest reduction in this parameter is about 65.1%. Employing the ribbed channel demonstrates smaller thermal entropy by generating six intense cross-flows. The highest reduction in the thermally generated entropy rate is around 72.9% when the triangular-shaped rib is used. Besides, the positive influence of the nanofluid is about 2.3 times higher when the ribbed channel is utilised. The triangular-shaped rib demonstrates better performance and considerably contributes to the lower thermal irreversibility. The overall irreversibility descends when the nanofluid is used and by an increase of Reynolds number.